Designing an ophthalmic progressive eyeglass by providing two progressive surfaces respectively on the two faces of the eyeglass is already known. In particular, using a progressive surface on either face of the eyeglass makes it possible to reduce the total amount of unwanted astigmatism of the eyeglass. To this purpose, both progressive surfaces are to be selected appropriately based on the locations and the directions of the unwanted astigmatism amounts which are produced respectively by the two surfaces.
Within the context of the present invention, a progressive eyeglass surface generally denotes a continuous surface which exhibits a variation in sphere between a far vision point and a near vision point pertaining to this surface. Then the addition is the difference in the sphere values between the far vision point and the near vision point. It is positive for an actually progressive surface, and negative for a regressive surface. In this specification, the phrase progressive surface is used for indicating both an actually progressive surface and a regressive surface, with the addition value being positive in the first case and negative in the second case.
Defining both progressive surfaces which are intended respectively for the front face and the back face of the ophthalmic eyeglass is a difficult task. It can be performed by optimizing each surface with point-to-point computation sequences, combined with calculating the value of a merit function. But such computation method is difficult to implement. It requires computation skill from the operator, complex computation means to be used and computation time. However such resources are not always available at the laboratory or at the retailer's office where the eyeglass is to be manufactured. As a consequence, it may not be possible to provide a progressive eyeglass wearer with the comfort improvements possible by implementing two progressive surfaces, one on either face of the eyeglass.
More precisely, surface optimization is an iterative computational process which involves target values for fixed features, at least one test surface, sequence for calculating values for the fixed features using the test surface, an algorithm for modifying the test surface and the merit function. The merit function enables to calculate a difference between the feature values for the test surface and the target values. This difference is reduced progressively by modifying the test surface at each iteration. The result of the optimization process is a new surface corresponding to a minimum in the values of the merit function. Although such process is called surface optimization, it is most often implemented with optical features. Such optical features may be optical power and unwanted astigmatism values for varying vision directions through an eyeglass, or other optical features which are derived from the optical power and unwanted astigmatism values. Anyway, the eyeglass optimization process implements again two-dimensional adjustments of the test eyeglass, so that the complexity of the process is unchanged. Because of this reason, such eyeglass optimization is usually called again surface optimization.
Surface optimization is different from surface derivation, this latter process being described in particular in U.S. Pat. No. 6,955,433. Basically, a surface derivation process consists in calculating surface coordinates from a distribution of sphere and cylinder values provided for this surface. Such calculation is a two-dimensional double integration process. Theoretically, a first integration step performed from the sphere and cylinder values leads to slope values of the surface, and a second integration step performed from the slope values leads to the surface sag values. Practically, both integration steps may be merged within a single computational step.
Therefore derivation of a final surface from an initial surface is comprised of three steps:
I\I calculating sphere and cylinder distributions for the initial surface; then
/ii/ transforming the sphere and cylinder distributions; then
/iiiV performing the two-dimensional double integration process from the sphere and cylinder distributions transformed, so as to obtain the final surface.
In a known manner, such surface derivation process may be implemented with any transformation type for the sphere and cylinder distributions used in step /ii/. One can cite the following transformations in particular:                any scaling operation applied to one or both base coordinates of the sag values of the initial surface;        any linear transformation applied to the sphere and cylinder values of the initial surface, including addition of a constant sphere value, so-called base value modification;        any spatially-limited modification of the sphere and cylinder values of the initial surface, including a change in the sphere values limited to a field around a near vision point, and resulting in addition value modification; and        any combination of the respective sphere and cylinder distributions of at least two initial surfaces, resulting into a new sphere and cylinder distribution which is assigned to the final surface.        